Abstract

Propagating and standing interfacial waves between a surface layer and an underlying half‐space, both under finite strain, are examined. The media are compressible nonlinear elastic and homogeneously pre‐strained with their principal axes of pre‐strain aligned, one axis being normal to the planar interface. For arbitrary strain energy functions and propagation along a principal axis of pre‐strain, the dispersion equation is obtained. A low‐frequency wave speed is subsequently obtained in explicit form yielding nonpropagation parameter conditions which for a specific state of stress hold at any frequency. The high‐frequency limit of the dispersion equation yields the secular equation for interfacial waves between two half‐spaces. It is then found that equal‐density compressible materials may allow propagation and that compressible materials with equal shear wave velocities parallel to the interface may filter interfacial waves, even under isotropic in‐plane stretching. For an arbitrary layer thickness as compared to the wavelength, material and pre‐strain parameter conditions are also derived for the existence of standing waves as solutions of the bifurcationequation, a limiting case of the dispersion equation.